Coverage for local/lib/python2.7/site-packages/sage/rings/monomials.py : 82%

"Monomials" 

def _monomials(gens, R, n, i): 

""" 

Given two lists ``gens`` and ``n`` of exactly the same length, 

return all monomials in the elements of ``gens`` in ``R`` where 

the ``i``-th generator in the monomial appears to degree strictly 

less than ``n[i]``. 

EXAMPLES:: 

sage: monomials([x], [3]) # indirect doctest 

[1, x, x^2] 

""" 

# each power of the ith generator times all products 

# not involving the ith generator. 

if len(gens) == 1: 

b = gens[0] 

v = [R(1)] 

for _ in range(n[0]-1): 

v.append(v[-1]*b) 

return v 

else: 

z = gens[i] 

w = list(gens) 

del w[i] 

nn = list(n) 

del nn[i] 

v = monomials(w, nn) 

k = len(v) 

for _ in range(n[i]-1): 

for j in range(k): 

v.append(v[j]*z) 

z *= gens[i] 

return v 

from sage.structure.sequence import Sequence 

def monomials(v, n): 

""" 

Given two lists ``v`` and ``n``, of exactly the same length, 

return all monomials in the elements of ``v``, where 

variable ``i`` (i.e., ``v[i]``) in the monomial appears to 

degree strictly less than ``n[i]``. 

INPUT: 

- ``v`` -- list of ring elements 

- ``n`` -- list of integers 

EXAMPLES:: 

sage: monomials([x], [3]) 

[1, x, x^2] 

sage: R.<x,y,z> = QQ[] 

sage: monomials([x,y], [5,5]) 

[1, y, y^2, y^3, y^4, x, x*y, x*y^2, x*y^3, x*y^4, x^2, x^2*y, x^2*y^2, x^2*y^3, x^2*y^4, x^3, x^3*y, x^3*y^2, x^3*y^3, x^3*y^4, x^4, x^4*y, x^4*y^2, x^4*y^3, x^4*y^4] 

sage: monomials([x,y,z], [2,3,2]) 

[1, z, y, y*z, y^2, y^2*z, x, x*z, x*y, x*y*z, x*y^2, x*y^2*z] 

""" 

if (len(v) != len(n)): 

raise ValueError("inputs must be of the same length.") 

if len(v) == 0: 

return [] 

v = Sequence(v) 

R = v.universe() 

return _monomials(v, R, n, 0)